Coupling coefficient of non idea transformer

[TS Liew]

Hi Fellas, many literature proposed to accept that the coupling coefficient of both side of the transformer to be the same. As such deriving the expression of mutual inductance M=K√L1L2. Base on the picture, what if Φ11≠Φ22 then K1≠K2 then M should be M=√K1K2L1L2 but I have not come across anyone suggesting so. My question: Is it a fact that K1 always = K2?

TS Liew (Electrical testing, Commissioning, Power system studies)